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Java example source code file (QuaternionTest.java)

This example Java source code file (QuaternionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

comparison_eps, eps, quaternion, quaterniontest, random, rotation, test, util, vector3d, zeroexception

The QuaternionTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.complex;

import java.util.Random;
import org.apache.commons.math3.complex.Quaternion;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.geometry.euclidean.threed.Rotation;
import org.apache.commons.math3.geometry.euclidean.threed.RotationConvention;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.util.FastMath;
import org.junit.Test;
import org.junit.Assert;

public class QuaternionTest {
    /** Epsilon for double comparison. */
    private static final double EPS = Math.ulp(1d);
    /** Epsilon for double comparison. */
    private static final double COMPARISON_EPS = 1e-14;

    @Test
    public final void testAccessors1() {
        final double q0 = 2;
        final double q1 = 5.4;
        final double q2 = 17;
        final double q3 = 0.0005;
        final Quaternion q = new Quaternion(q0, q1, q2, q3);

        Assert.assertEquals(q0, q.getQ0(), 0);
        Assert.assertEquals(q1, q.getQ1(), 0);
        Assert.assertEquals(q2, q.getQ2(), 0);
        Assert.assertEquals(q3, q.getQ3(), 0);
    }

    @Test
    public final void testAccessors2() {
        final double q0 = 2;
        final double q1 = 5.4;
        final double q2 = 17;
        final double q3 = 0.0005;
        final Quaternion q = new Quaternion(q0, q1, q2, q3);

        final double sP = q.getScalarPart();
        final double[] vP = q.getVectorPart();

        Assert.assertEquals(q0, sP, 0);
        Assert.assertEquals(q1, vP[0], 0);
        Assert.assertEquals(q2, vP[1], 0);
        Assert.assertEquals(q3, vP[2], 0);
    }

    @Test
    public final void testAccessors3() {
        final double q0 = 2;
        final double q1 = 5.4;
        final double q2 = 17;
        final double q3 = 0.0005;
        final Quaternion q = new Quaternion(q0, new double[] { q1, q2, q3 });

        final double sP = q.getScalarPart();
        final double[] vP = q.getVectorPart();

        Assert.assertEquals(q0, sP, 0);
        Assert.assertEquals(q1, vP[0], 0);
        Assert.assertEquals(q2, vP[1], 0);
        Assert.assertEquals(q3, vP[2], 0);
    }

    @Test(expected=DimensionMismatchException.class)
    public void testWrongDimension() {
        new Quaternion(new double[] { 1, 2 });
    }

    @Test
    public final void testConjugate() {
        final double q0 = 2;
        final double q1 = 5.4;
        final double q2 = 17;
        final double q3 = 0.0005;
        final Quaternion q = new Quaternion(q0, q1, q2, q3);

        final Quaternion qConjugate = q.getConjugate();

        Assert.assertEquals(q0, qConjugate.getQ0(), 0);
        Assert.assertEquals(-q1, qConjugate.getQ1(), 0);
        Assert.assertEquals(-q2, qConjugate.getQ2(), 0);
        Assert.assertEquals(-q3, qConjugate.getQ3(), 0);
    }

    @Test
    public final void testProductQuaternionQuaternion() {

        // Case : analytic test case

        final Quaternion qA = new Quaternion(1, 0.5, -3, 4);
        final Quaternion qB = new Quaternion(6, 2, 1, -9);
        final Quaternion qResult = Quaternion.multiply(qA, qB);

        Assert.assertEquals(44, qResult.getQ0(), EPS);
        Assert.assertEquals(28, qResult.getQ1(), EPS);
        Assert.assertEquals(-4.5, qResult.getQ2(), EPS);
        Assert.assertEquals(21.5, qResult.getQ3(), EPS);

        // comparison with the result given by the formula :
        // qResult = (scalarA * scalarB - vectorA . vectorB) + (scalarA * vectorB + scalarB * vectorA + vectorA ^
        // vectorB)

        final Vector3D vectorA = new Vector3D(qA.getVectorPart());
        final Vector3D vectorB = new Vector3D(qB.getVectorPart());
        final Vector3D vectorResult = new Vector3D(qResult.getVectorPart());

        final double scalarPartRef = qA.getScalarPart() * qB.getScalarPart() - Vector3D.dotProduct(vectorA, vectorB);

        Assert.assertEquals(scalarPartRef, qResult.getScalarPart(), EPS);

        final Vector3D vectorPartRef = ((vectorA.scalarMultiply(qB.getScalarPart())).add(vectorB.scalarMultiply(qA
                .getScalarPart()))).add(Vector3D.crossProduct(vectorA, vectorB));
        final double norm = (vectorResult.subtract(vectorPartRef)).getNorm();

        Assert.assertEquals(0, norm, EPS);

        // Conjugate of the product of two quaternions and product of their conjugates :
        // Conj(qA * qB) = Conj(qB) * Conj(qA)

        final Quaternion conjugateOfProduct = qB.getConjugate().multiply(qA.getConjugate());
        final Quaternion productOfConjugate = (qA.multiply(qB)).getConjugate();

        Assert.assertEquals(conjugateOfProduct.getQ0(), productOfConjugate.getQ0(), EPS);
        Assert.assertEquals(conjugateOfProduct.getQ1(), productOfConjugate.getQ1(), EPS);
        Assert.assertEquals(conjugateOfProduct.getQ2(), productOfConjugate.getQ2(), EPS);
        Assert.assertEquals(conjugateOfProduct.getQ3(), productOfConjugate.getQ3(), EPS);
    }

    @Test
    public final void testProductQuaternionVector() {

        // Case : Product between a vector and a quaternion : QxV

        final Quaternion quaternion = new Quaternion(4, 7, -1, 2);
        final double[] vector = {2.0, 1.0, 3.0};
        final Quaternion qResultQxV = Quaternion.multiply(quaternion, new Quaternion(vector));

        Assert.assertEquals(-19, qResultQxV.getQ0(), EPS);
        Assert.assertEquals(3, qResultQxV.getQ1(), EPS);
        Assert.assertEquals(-13, qResultQxV.getQ2(), EPS);
        Assert.assertEquals(21, qResultQxV.getQ3(), EPS);

        // comparison with the result given by the formula :
        // qResult = (- vectorQ . vector) + (scalarQ * vector + vectorQ ^ vector)

        final double[] vectorQ = quaternion.getVectorPart();
        final double[] vectorResultQxV = qResultQxV.getVectorPart();

        final double scalarPartRefQxV = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector));
        Assert.assertEquals(scalarPartRefQxV, qResultQxV.getScalarPart(), EPS);

        final Vector3D vectorPartRefQxV = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D
                .crossProduct(new Vector3D(vectorQ), new Vector3D(vector)));
        final double normQxV = (new Vector3D(vectorResultQxV).subtract(vectorPartRefQxV)).getNorm();
        Assert.assertEquals(0, normQxV, EPS);

        // Case : Product between a vector and a quaternion : VxQ

        final Quaternion qResultVxQ = Quaternion.multiply(new Quaternion(vector), quaternion);

        Assert.assertEquals(-19, qResultVxQ.getQ0(), EPS);
        Assert.assertEquals(13, qResultVxQ.getQ1(), EPS);
        Assert.assertEquals(21, qResultVxQ.getQ2(), EPS);
        Assert.assertEquals(3, qResultVxQ.getQ3(), EPS);

        final double[] vectorResultVxQ = qResultVxQ.getVectorPart();

        // comparison with the result given by the formula :
        // qResult = (- vector . vectorQ) + (scalarQ * vector + vector ^ vectorQ)

        final double scalarPartRefVxQ = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector));
        Assert.assertEquals(scalarPartRefVxQ, qResultVxQ.getScalarPart(), EPS);

        final Vector3D vectorPartRefVxQ = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D
                .crossProduct(new Vector3D(vector), new Vector3D(vectorQ)));
        final double normVxQ = (new Vector3D(vectorResultVxQ).subtract(vectorPartRefVxQ)).getNorm();
        Assert.assertEquals(0, normVxQ, EPS);
    }

    @Test
    public final void testDotProductQuaternionQuaternion() {
        // expected output
        final double expected = -6.;
        // inputs
        final Quaternion q1 = new Quaternion(1, 2, 2, 1);
        final Quaternion q2 = new Quaternion(3, -2, -1, -3);

        final double actual1 = Quaternion.dotProduct(q1, q2);
        final double actual2 = q1.dotProduct(q2);

        Assert.assertEquals(expected, actual1, EPS);
        Assert.assertEquals(expected, actual2, EPS);
    }

    @Test
    public final void testScalarMultiplyDouble() {
        // expected outputs
        final double w = 1.6;
        final double x = -4.8;
        final double y = 11.20;
        final double z = 2.56;
        // inputs
        final Quaternion q1 = new Quaternion(0.5, -1.5, 3.5, 0.8);
        final double a = 3.2;

        final Quaternion q = q1.multiply(a);

        Assert.assertEquals(w, q.getQ0(), COMPARISON_EPS);
        Assert.assertEquals(x, q.getQ1(), COMPARISON_EPS);
        Assert.assertEquals(y, q.getQ2(), COMPARISON_EPS);
        Assert.assertEquals(z, q.getQ3(), COMPARISON_EPS);
    }

    @Test
    public final void testAddQuaternionQuaternion() {
        // expected outputs
        final double w = 4;
        final double x = -1;
        final double y = 2;
        final double z = -4;
        // inputs
        final Quaternion q1 = new Quaternion(1., 2., -2., -1.);
        final Quaternion q2 = new Quaternion(3., -3., 4., -3.);

        final Quaternion qa = Quaternion.add(q1, q2);
        final Quaternion qb = q1.add(q2);

        Assert.assertEquals(w, qa.getQ0(), EPS);
        Assert.assertEquals(x, qa.getQ1(), EPS);
        Assert.assertEquals(y, qa.getQ2(), EPS);
        Assert.assertEquals(z, qa.getQ3(), EPS);

        Assert.assertEquals(w, qb.getQ0(), EPS);
        Assert.assertEquals(x, qb.getQ1(), EPS);
        Assert.assertEquals(y, qb.getQ2(), EPS);
        Assert.assertEquals(z, qb.getQ3(), EPS);
    }

    @Test
    public final void testSubtractQuaternionQuaternion() {
        // expected outputs
        final double w = -2.;
        final double x = 5.;
        final double y = -6.;
        final double z = 2.;
        // inputs
        final Quaternion q1 = new Quaternion(1., 2., -2., -1.);
        final Quaternion q2 = new Quaternion(3., -3., 4., -3.);

        final Quaternion qa = Quaternion.subtract(q1, q2);
        final Quaternion qb = q1.subtract(q2);

        Assert.assertEquals(w, qa.getQ0(), EPS);
        Assert.assertEquals(x, qa.getQ1(), EPS);
        Assert.assertEquals(y, qa.getQ2(), EPS);
        Assert.assertEquals(z, qa.getQ3(), EPS);

        Assert.assertEquals(w, qb.getQ0(), EPS);
        Assert.assertEquals(x, qb.getQ1(), EPS);
        Assert.assertEquals(y, qb.getQ2(), EPS);
        Assert.assertEquals(z, qb.getQ3(), EPS);
}

    @Test
    public final void testNorm() {

        final double q0 = 2;
        final double q1 = 1;
        final double q2 = -4;
        final double q3 = 3;
        final Quaternion q = new Quaternion(q0, q1, q2, q3);

        final double norm = q.getNorm();

        Assert.assertEquals(FastMath.sqrt(30), norm, 0);

        final double normSquareRef = Quaternion.multiply(q, q.getConjugate()).getScalarPart();
        Assert.assertEquals(FastMath.sqrt(normSquareRef), norm, 0);
    }

    @Test
    public final void testNormalize() {

        final Quaternion q = new Quaternion(2, 1, -4, -2);

        final Quaternion versor = q.normalize();

        Assert.assertEquals(2.0 / 5.0, versor.getQ0(), 0);
        Assert.assertEquals(1.0 / 5.0, versor.getQ1(), 0);
        Assert.assertEquals(-4.0 / 5.0, versor.getQ2(), 0);
        Assert.assertEquals(-2.0 / 5.0, versor.getQ3(), 0);

        Assert.assertEquals(1, versor.getNorm(), 0);
    }

    @Test(expected=ZeroException.class)
    public final void testNormalizeFail() {
        final Quaternion zeroQ = new Quaternion(0, 0, 0, 0);
        zeroQ.normalize();
    }

    @Test
    public final void testObjectEquals() {
        final double one = 1;
        final Quaternion q1 = new Quaternion(one, one, one, one);
        Assert.assertTrue(q1.equals(q1));

        final Quaternion q2 = new Quaternion(one, one, one, one);
        Assert.assertTrue(q2.equals(q1));

        final Quaternion q3 = new Quaternion(one, FastMath.nextUp(one), one, one);
        Assert.assertFalse(q3.equals(q1));
    }

    @Test
    public final void testQuaternionEquals() {
        final double inc = 1e-5;
        final Quaternion q1 = new Quaternion(2, 1, -4, -2);
        final Quaternion q2 = new Quaternion(q1.getQ0() + inc, q1.getQ1(), q1.getQ2(), q1.getQ3());
        final Quaternion q3 = new Quaternion(q1.getQ0(), q1.getQ1() + inc, q1.getQ2(), q1.getQ3());
        final Quaternion q4 = new Quaternion(q1.getQ0(), q1.getQ1(), q1.getQ2() + inc, q1.getQ3());
        final Quaternion q5 = new Quaternion(q1.getQ0(), q1.getQ1(), q1.getQ2(), q1.getQ3() + inc);

        Assert.assertFalse(q1.equals(q2, 0.9 * inc));
        Assert.assertFalse(q1.equals(q3, 0.9 * inc));
        Assert.assertFalse(q1.equals(q4, 0.9 * inc));
        Assert.assertFalse(q1.equals(q5, 0.9 * inc));

        Assert.assertTrue(q1.equals(q2, 1.1 * inc));
        Assert.assertTrue(q1.equals(q3, 1.1 * inc));
        Assert.assertTrue(q1.equals(q4, 1.1 * inc));
        Assert.assertTrue(q1.equals(q5, 1.1 * inc));
    }

    @Test
    public final void testQuaternionEquals2() {
        final Quaternion q1 = new Quaternion(1, 4, 2, 3);
        final double gap = 1e-5;
        final Quaternion q2 = new Quaternion(1 + gap, 4 + gap, 2 + gap, 3 + gap);

        Assert.assertTrue(q1.equals(q2, 10 * gap));
        Assert.assertFalse(q1.equals(q2, gap));
        Assert.assertFalse(q1.equals(q2, gap / 10));
    }

    @Test
    public final void testIsUnitQuaternion() {
        final Random r = new Random(48);
        final int numberOfTrials = 1000;
        for (int i = 0; i < numberOfTrials; i++) {
            final Quaternion q1 = new Quaternion(r.nextDouble(), r.nextDouble(), r.nextDouble(), r.nextDouble());
            final Quaternion q2 = q1.normalize();
            Assert.assertTrue(q2.isUnitQuaternion(COMPARISON_EPS));
        }

        final Quaternion q = new Quaternion(1, 1, 1, 1);
        Assert.assertFalse(q.isUnitQuaternion(COMPARISON_EPS));
    }

    @Test
    public final void testIsPureQuaternion() {
        final Quaternion q1 = new Quaternion(0, 5, 4, 8);
        Assert.assertTrue(q1.isPureQuaternion(EPS));

        final Quaternion q2 = new Quaternion(0 - EPS, 5, 4, 8);
        Assert.assertTrue(q2.isPureQuaternion(EPS));

        final Quaternion q3 = new Quaternion(0 - 1.1 * EPS, 5, 4, 8);
        Assert.assertFalse(q3.isPureQuaternion(EPS));

        final Random r = new Random(48);
        final double[] v = {r.nextDouble(), r.nextDouble(), r.nextDouble()};
        final Quaternion q4 = new Quaternion(v);
        Assert.assertTrue(q4.isPureQuaternion(0));

        final Quaternion q5 = new Quaternion(0, v);
        Assert.assertTrue(q5.isPureQuaternion(0));
    }

    @Test
    public final void testPolarForm() {
        final Random r = new Random(48);
        final int numberOfTrials = 1000;
        for (int i = 0; i < numberOfTrials; i++) {
            final Quaternion q = new Quaternion(2 * (r.nextDouble() - 0.5), 2 * (r.nextDouble() - 0.5),
                                                2 * (r.nextDouble() - 0.5), 2 * (r.nextDouble() - 0.5));
            final Quaternion qP = q.getPositivePolarForm();

            Assert.assertTrue(qP.isUnitQuaternion(COMPARISON_EPS));
            Assert.assertTrue(qP.getQ0() >= 0);

            final Rotation rot = new Rotation(q.getQ0(), q.getQ1(), q.getQ2(), q.getQ3(), true);
            final Rotation rotP = new Rotation(qP.getQ0(), qP.getQ1(), qP.getQ2(), qP.getQ3(), true);

            Assert.assertEquals(rot.getAngle(), rotP.getAngle(), COMPARISON_EPS);
            Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getX(),
                                rot.getAxis(RotationConvention.VECTOR_OPERATOR).getX(),
                                COMPARISON_EPS);
            Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getY(),
                                rot.getAxis(RotationConvention.VECTOR_OPERATOR).getY(),
                                COMPARISON_EPS);
            Assert.assertEquals(rot.getAxis(RotationConvention.VECTOR_OPERATOR).getZ(),
                                rot.getAxis(RotationConvention.VECTOR_OPERATOR).getZ(),
                                COMPARISON_EPS);
        }
    }

    @Test
    public final void testGetInverse() {
        final Quaternion q = new Quaternion(1.5, 4, 2, -2.5);

        final Quaternion inverseQ = q.getInverse();
        Assert.assertEquals(1.5 / 28.5, inverseQ.getQ0(), 0);
        Assert.assertEquals(-4.0 / 28.5, inverseQ.getQ1(), 0);
        Assert.assertEquals(-2.0 / 28.5, inverseQ.getQ2(), 0);
        Assert.assertEquals(2.5 / 28.5, inverseQ.getQ3(), 0);

        final Quaternion product = Quaternion.multiply(inverseQ, q);
        Assert.assertEquals(1, product.getQ0(), EPS);
        Assert.assertEquals(0, product.getQ1(), EPS);
        Assert.assertEquals(0, product.getQ2(), EPS);
        Assert.assertEquals(0, product.getQ3(), EPS);

        final Quaternion qNul = new Quaternion(0, 0, 0, 0);
        try {
            final Quaternion inverseQNul = qNul.getInverse();
            Assert.fail("expecting ZeroException but got : " + inverseQNul);
        } catch (ZeroException ex) {
            // expected
        }
    }

    @Test
    public final void testToString() {
        final Quaternion q = new Quaternion(1, 2, 3, 4);
        Assert.assertTrue(q.toString().equals("[1.0 2.0 3.0 4.0]"));
    }
}

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